A bench headed by Chief Justice D Y Chandrachud also sought response of priest Shailendra Kumar Pathak Vyas by April 30 on the plea of the mosque committee.
The plea filed by the Hindu side has stated that the cellar's roof is very old and weak.
The Allahabad high court on Friday did not give any immediate relief to the Gyanvapi Masjid committee which had challenged the order of the Varanasi court allowing Hindu prayers in a cellar of the mosque.
Earlier on Wednesday, the district court ruled that a priest can perform prayers before the idols in a cellar of the Gyanvapi Masjid, a significant development in the legal battle over the mosque adjacent to the Kashi Vishwanath temple.
In the appeal filed before the high court, it has been pleaded that the Hindu side's suit itself is barred by order 7 rule 11 of the Civil Procedure Code, Naqvi said.
The high court has dismissed the Gyanvapi mosque management committee's appeal.
Four persons have died in Bihar since Monday in rain-related incidents due to the 'peripheral effect' of Cyclone Phailin, taking the death toll in the state to 14.
According to media reports, 56 people -- mostly farm labourers working in the fields -- died in Bihar while 44 people were killed across Uttar Pradesh, Jharkand and Madhya Pradesh.